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MATH

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(2,14),(1,-1),(3,35)

Find the quadratic function y=ax^2+bx+c

1) 4a+2b+c=14
2) a+b+c=-1
3) 9a+3b+c= 35

equation 1&2 = 3a + b = 13
equation 1&3 = -5a +5b = -21

  • MATH -

    It is easier if you write y as:


    y = A (x-1)(x-3) + B(x-2)(x-3) +
    C(x-2)(x-1)

    y(1) = -1 ---->

    2 B = -1 --->

    B = -1/2


    y(2) = 14 ------->

    A = -14


    y(3) = 35 --------->

    C = 35/2

    So, we have:

    y = -14(x-1)(x-3) -1/2 (x-2)(x-3) +
    35/2 (x-2)(x-1) =

    3 x^2 + 6 x -10

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